We consider the spin-1/2 isotropic $XY$ chain in an external magnetic field directed along $z$ axis with periodically varying $g$-factors. To reveal the effects of regularly alternating $g$-factors, we calculate various static and dynamic equilibrium quantities in the ground state and at finite temperatures. We demonstrate that because of the regularly alternating $g$-factors the saturation field may disappear and the field dependence of the susceptibility in the ground state has additional logarithmic singularity at zero field. Moreover, the zero-field susceptibility has a logarithmic singularity as $T\to 0$. Furthermore, the dynamic structure factors exhibit much more structure in the "wave vector -- frequency" plane that can be traced out to modifications of the two-fermion excitation continua which exclusively determine $S_{zz}(κ,ω)$ and dominate the properties of $S_{xx}(κ,ω)$. We discuss what changes can be observed in dynamic experiments on the corresponding substances.
The effect of the canting of local anisotropy axes on the ground-state phase diagram and magnetization of a ferrimagnetic chain with regularly alternating Ising and Heisenberg spins is exactly examined in an arbitrarily oriented magnetic field. It is shown that individual contributions of Ising and Heisenberg spins to the total magnetization basically depend on the spatial orientation of the magnetic field and the canting angle between two different local anisotropy axes of the Ising spins.
Using the Jordan-Wigner transformation and continued fractions we calculate rigorously the thermodynamic quantities for the spin-1/2 transverse Ising chain with periodically varying intersite interactions and/or on-site fields. We consider in detail the properties of the chains having a period of the transverse field modulation equal to 3. The regularly alternating transverse Ising chain exhibits several quantum phase transition points, where the number of transition points for a given period of alternation strongly depends on the specific set of the Hamiltonian parameters. The critical behavi…
We consider the ground-state properties of the s=1/2 Ising chain in a transverse field which varies regularly along the chain having a period of alternation 2. Such a model, similarly to its uniform counterpart, exhibits quantum phase transitions. However, the number and the position of the quantum phase transition points depend on the strength of transverse field modulation. The behaviour in the vicinity of the critical field in most cases remains the same as for the uniform chain (i.e. belongs to the square-lattice Ising model universality class). However, a new critical behaviour may also a…
Using rigorous analytical analysis and exact numerical data for the spin-1/2 transverse Ising chain we discuss the effects of regular alternation of the Hamiltonian parameters on the quantum phase transition inherent in the model.
A classical-quantum chain composed of regularly alternating Ising and Heisenberg spins is rigorously solved by considering two distinct local anisotropy axes of the Ising spins. The ground-state phase diagram and magnetization curves are examined depending on a spatial orientation of the applied magnetic field. The phase diagram totally consists of four distinct phases and a few macroscopically degenerate points, where an outstanding coexistence of perfect order and complete disorder occurs within the so-called 'half-fire, half-ice' state. The zero-temperature magnetization curves generally ex…
The magnetic behaviors of a spin-1/2 alternating Heisenberg antiferromagnetic chain in a staggered transverse magnetic field is studied by means of the density-matrix renormalization group method and Jordan-Wigner transformation. Quantum phase transitions of different types are observed in the S=1 Neel and XY-like gapless phases, which result from the competitions between the staggered transverse field and magnetic orders induced by anisotropy and alternating interactions. The results are compared with the mean-field and some exactly resolved results.
We calculate dynamical structure factors of the S=1 bond-alternating Heisenberg chain with a single-ion anisotropy in transverse magnetic fields, using a continued fraction method based on the Lanczos algorithm. In the Haldane-gap phase and the dimer phase, dynamical structure factors show characteristic field dependence. Possible interpretations are discussed. The numerical results are in qualitative agreement with recent results for inelastic neutron-scattering experiments on the S=1 bond-alternating Heisenberg-chain compound $\rm{Ni(C_{9}D_{24}N_{4})(NO_{2})ClO_{4}}$ and the S=1 Haldane-gap…
The ground state phase diagram of the alternating spin-1/2 chains with anisotropic ferromagnetic coupling under the influence of a symmetry breaking transverse magnetic field is studied. We have used the exact diagonalization technique. In the limit where the antiferromagnetic coupling is dominant, we have identified two Ising-type quantum phase transitions. We have calculated two critical fields $h_{c_{1}}$ and $h_{c_{2}}$, corresponding to the transition between different magnetic phases of the system. It is found that the intermediate state ($h_{c_{1}}<h<h_{c_{2}}$) is gapful, describing th…
The ground state phase diagrams and thermodynamic properties of a spin-1 bond-alternating Heisenberg antiferromagnetic chain with a single-ion anisotropy in longitudinal and transverse magnetic fields are investigated jointly by means of the infinite time evolving block decimation, the linearized tensor renormalization group and the density matrix renormalization group methods. It is found that in the magnetic field-bond alternating ratio plane six phases such as singlet dimer, Haldane, two Tomonaga-Luttinger liquid, 1/2 magnetization plateau and spin polarized phases are identified in a longi…
We have studied the zero and low-temperature behavior of anisotropic alternating antiferromagnetic-ferromagnetic Heisenberg spin-1/2 chains in a transverse magnetic field. Using the analytical spinless fermion approach, the thermodynamic behavior of the model has been studied. We have introduced a new order parameter to distinguish the gapless Luttinger liquid phase from the other gapped phases. The exact diagonalization Lanczos results are also used to compare with the spinless fermion ones. We have found a double peak structure in the specific heat curves for the region between the two quant…
We report all phases and corresponding critical lines of the quantum anisotropic transverse XY model with Dzyaloshinskii-Moriya (DM) interaction along with uniform and alternating transverse magnetic fields (ATXY) by using appropriately chosen order parameters. We prove that when DM interaction is weaker than the anisotropy parameter, it has no effect at all on the zero-temperature states of the XY model with uniform transverse magnetic field which is not the case for the ATXY model. However, when DM interaction is stronger than the anisotropy parameter, we show appearance of a new gapless pha…
The ferrimagnetic spin-1/2 chain composed of alternating Ising and Heisenberg spins in an arbitrarily oriented magnetic field is exactly solved using the spin-rotation transformation and the transfer-matrix method. It is shown that the low-temperature magnetization process depends basically on a spatial orientation of the magnetic field. A sharp stepwise magnetization curve with a marked intermediate plateau, which emerges for the magnetic field applied along the easy-axis direction of the Ising spins, becomes smoother and the intermediate plateau shrinks if the external field is tilted from t…
We consider an alternating Heisenberg spin-$1/2$ antiferromagnetic-ferromagnetic ($AF-F$) chain with the space modulated dominant antiferromagnetic exchange and anisotropic ferromagnetic coupling (tetrameric spin-$1/2$ chain). The zero-temperature effect of a symmetry breaking transverse magnetic field on the model is studied numerically. It is found that the anisotropy effect on the ferromagnetic coupling induces two new gapped phases. We identified their orderings as a kind of the stripe-antiferromagnetic phase. As a result, the magnetic phase diagram of the tetrameric chain shows five gappe…
We calculate the ground-state compressibility of a deformable spin-1/2 Heisenberg-Ising chain with Dzyaloshinskii-Moriya interaction to discuss how a quantum critical point inherent in this spin system may manifest itself in the elastic properties of the underlying lattice. We compare these results with the corresponding ones for the spin-1/2 Ising chain in a longitudinal or transverse field and the spin-1/2 $XX$ chain in a transverse field. The inverse compressibility of the spin-1/2 $XX$ chain in a transverse field exhibits a hysteresis in a vicinity of quantum critical point that is accompa…
The dynamical structure factor of the S=1/2 bond-alternating spin chain with a next-nearest-neighbor interaction in magnetic field is investigated using the continued fraction method based on the Lanczos algorithm. When the plateau exists on the magnetization curve, the longitudinal dynamical structure factor shows a large intensity with a periodic dispersion relation, while the transverse one shows a large intensity with an almost dispersionless mode. The periodicity and the amplitude of the dispersion relation in the longitudinal dynamical structure factor are sensitive to the coupling const…
We investigate quantum phase transitions and quantum coherence in a quantum compass chain under an alternating transverse magnetic field. The model can be analytically solved by the Jordan-Wigner transformation and this solution shows that it is equivalent to a two-component one-dimensional (1D) Fermi gas on a lattice. We explore mutual effects of the staggered magnetic interaction and multi-site interactions on the energy spectra and analyze the ground state phase diagram. We use quantum coherence measures to identify the quantum phase transitions. Our results show that $l_1$ norm of coherenc…
We investigate the static and dynamical patterns of entanglement in an anisotropic XY model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse XY model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a "factorization line" on the plane of sys…
Typically two particles (spins) could be maximally entangled at zero temperature, and for a certain temperature the phenomenon of entanglement vanishes at the threshold temperature. For the Heisenberg coupled model or even the Ising model with a transverse magnetic field, one can observe some rise of entanglement even for a disentangled region at zero temperature. So we can understand this emergence of entanglement at finite temperature as being due to the mixing of some maximally entangled states with some other untangled states. Here, we present a simple one-dimensional Ising model with alte…
Block entanglement entropy in the ground state of a quantum spin chain is investigated. The spins have Kitaev-type nearest-neighbor interaction, of strength J_x or J_y, through either x or y components of the spins on alternating bonds, along with a transverse magnetic field h. An exact solution is obtained through Jordan-Wigner fermionization, and it exhibits a macroscopically degenerate ground state for h=0, and a non-degenerate ground state for nonzero h and for all interaction strengths. For a chain of N spins, we study the block entropy of a partition of L contiguous spins. The block enta…
We analyze instabilities of the collinear up-up-down state of a two-dimensional quantum spin-S spatially anisotropic triangular lattice antiferromagnet in a magnetic field. We find, within large-S approximation, that near the end point of the plateau, the collinear state becomes unstable due to condensation of two-magnon bound pairs rather than single magnons. The two-magnon instability leads to a novel 2D vector chiral phase with alternating spin currents but no magnetic order in the direction transverse to the field. This phase breaks a discrete Z_2 symmetry but preserves a continuous U(1) o…
The Ising chain in transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, topological defects, quantum criticality, and duality. Although the quasi-1D ferromagnet CoNb$_2$O$_6$ has been put forward as the best material example of the transverse field Ising model, it exhibits significant deviations from ideality. Through a combination of THz spectroscopy and theory, we show that CoNb$_2$O$_6$ in fact is well described by a different model with strong bond dependent interactions, which we dub the {\it twisted Kitaev chain}, as these in…
We study the emergence of exact Majorana zero modes (EMZMs) in a one-dimensional quantum transverse compass model with both the nearest-neighbor interactions and transverse fields varying over space. By transforming the spin system into a quadratic Majorana-fermion model, we derive an exact formula for the number of the emergent EMZMs, which is found to depend on the partition nature of the lattice sites on which the magnetic fields vanish. We also derive explicit expressions for the wavefunctions of these EMZMs and show that they indeed depend on fine features of the foregoing partition of si…
Ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed to the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg-Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the 'classical' Ising chain in a longitudinal field or th…
Magnetic excitations in copper pyrimidine dinitrate, a spin-1/2 antiferromagnetic chain with alternating $g$-tensor and Dzyaloshinskii-Moriya interactions that exhibits a field-induced spin gap, are probed by means of pulsed-field electron spin resonance spectroscopy. In particular, we report on a minimum of the gap in the vicinity of the saturation field $H_{sat}=48.5$ T associated with a transition from the sine-Gordon region (with soliton-breather elementary excitations) to a spin-polarized state (with magnon excitations). This interpretation is fully confirmed by the quantitative agreement…
Effects of single-site anisotropy on mixed diamond chains with spins 1 and 1/2 are investigated in the ground states and at finite temperatures. There are phases where the ground state is a spin cluster solid, i.e., an array of uncorrelated spin-1 clusters separated by singlet dimers. The ground state is nonmagnetic for the easy-plane anisotropy, while it is paramagnetic for the easy-axis anisotropy. Also, there are the Néel, Haldane, and large-$D$ phases, where the ground state is a single spin cluster of infinite size and the system is equivalent to the spin-1 Heisenberg chain with alternati…
The entanglement and quantum correlation measures have been investigated for the ground state of a spin chain with a Kitaev-type exchange interactions on alternating bonds, along with a transverse magnetic field. There is a macroscopic degeneracy in the ground state for zero magnetic field, implying a quantum critical point. But peculiarly in this model, the entanglement measures do not show any singular behavior in the vicinity of the critical point, as seen in the transverse Ising model ground state and related models. We have investigated different correlation measures analytically, that ha…
